I gave address to my partner about a year ago. Can he/she make transaction on this address?
Yes.
Is it possible to generate several addresses for future (year or several years later) usage?
Yes.
Is there any limitation of lifespan for BTC addresses?
No.
I know there is a limitation of how many address you can create although don't know the exact number.
There's no limit. I've created millions of addresses (and only used a few). Just make sure you secure the private key and/or wallet seed, make enough backups, keep them safe, and keep a note on how to use them later. Too many topics pop up lately from people who don't remember how to use their old backups.